Estimating the Effective Reproduction Number of COVID-19 in South Africa
Louis Rossouw
2020-10-29
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 6aa94557d03c9127396e4f54895aa31f35e44463.
2 Data
Data is downloaded from the Git repository associated with [3]. This contains the daily cases and deaths reported by the NICD for South Africa by province. The data is somewhat problematic as it does not contain data by date of test or date of death but by reporting date. It’s not clear what the reporting delays are and they may be significant (especially for the deaths).
In the case data file row 21 and 32 contain no provincial details. We estimated it by spreading the national total to the provinces in proportion to the combined mixture of the prior day and the next day.
Further fixes are applied to both case and death data:
- Scale up the per province data for unknown values.
- This results in provincial data which are not whole numbers. These are rounded to the nearest whole number.
- A
SAcolumn is added as the sum of the new per province data. - Data is formatted and disaggregated such that item represents the incremental cases or deaths rather than cumulative figures.
- Data is filled with data (albeit with 0 cases or deaths) for all dates in the range.
- Any incremental case or death counts that are negative are set to zero.
- New cumulative figures are calculated.
3 Methodology
The methodology is described in detail here.
4 Results
4.1 Cases and Deaths
Below we plot cumulative case count on a log scale by province:
Below we plot the cumulative deaths by province on a log scale:
4.2 Current \(R_{t,m}\) estimates by Province
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| province | Estimated Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| EC | cases | 2,484 | 2020-10-28 | 1.4 | 1.5 | 1.6 |
| EC | deaths | 80 | 2020-10-28 | 0.5 | 0.6 | 0.8 |
| FS | cases | 1,958 | 2020-10-28 | 0.8 | 0.9 | 0.9 |
| FS | deaths | 91 | 2020-10-28 | 0.6 | 0.7 | 0.9 |
| GP | cases | 1,760 | 2020-10-28 | 0.9 | 0.9 | 0.9 |
| GP | deaths | 34 | 2020-10-28 | 0.2 | 0.3 | 0.4 |
| KZN | cases | 977 | 2020-10-28 | 1.0 | 1.0 | 1.1 |
| KZN | deaths | 49 | 2020-10-28 | 0.4 | 0.5 | 0.7 |
| LP | cases | 418 | 2020-10-28 | 0.9 | 1.0 | 1.0 |
| LP | deaths | 18 | 2020-10-28 | 0.7 | 1.2 | 1.8 |
| MP | cases | 530 | 2020-10-28 | 0.9 | 1.0 | 1.0 |
| MP | deaths | 9 | 2020-10-28 | 0.6 | 1.3 | 2.3 |
| NC | cases | 870 | 2020-10-28 | 0.8 | 0.8 | 0.9 |
| NC | deaths | 6 | 2020-10-28 | 0.2 | 0.6 | 1.0 |
| NW | cases | 754 | 2020-10-28 | 0.8 | 0.9 | 0.9 |
| NW | deaths | 31 | 2020-10-28 | 1.3 | 1.8 | 2.3 |
| WC | cases | 1,604 | 2020-10-28 | 1.0 | 1.0 | 1.1 |
| WC | deaths | 52 | 2020-10-28 | 1.0 | 1.3 | 1.7 |
| SA | cases | 11,355 | 2020-10-28 | 1.0 | 1.0 | 1.0 |
| SA | deaths | 370 | 2020-10-28 | 0.7 | 0.7 | 0.8 |
Estimated Effective Reproduction Number by Province
4.3 Maps of Effective Reproduction Number
Below estimates of the reproductive number is plotted on maps of South Africa [4].
4.3.1 Cases
4.3.2 Deaths
4.4 Estimated Effective Reproduction Number for South Africa over Time
Below we plot results for South Africa as a whole.
Estimated Effective Reproduction Number for South Africa over Time
4.5 Estimated Effective Reproduction Number for Provinces over Time
Below we plot results for each province. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
4.5.1 Eastern Cape
Estimated Effective Reproduction Number for Eastern Cape over Time
4.5.2 Free State
Estimated Effective Reproduction Number for Free State over Time
4.5.3 Gauteng
Estimated Effective Reproduction Number for Gauteng over Time
4.5.4 KwaZulu-Natal
Estimated Effective Reproduction Number for KwaZulu-Natal over Time
4.5.5 Limpopo
Estimated Effective Reproduction Number for Limpopo over Time
4.5.6 Mpumalanga
Estimated Effective Reproduction Number for Mpumalanga over Time
4.5.7 Northern Cape
Estimated Effective Reproduction Number for Northern Cape over Time
4.5.8 North West
Estimated Effective Reproduction Number for Gauteng over Time
4.5.9 Western Cape
Estimated Effective Reproduction Number for Western Cape over Time
4.6 Detailed Results
Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.
5 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed serial interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection, more so in the case of the use of deaths.
- It’s sensitive to changes in case (or death) detection.
- The serial interval may change over time.
Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.
Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.
References
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] V. Marivate et al., “Coronavirus disease (COVID-19) case data - South Africa.” Zenodo, 21-Mar-2020 [Online]. Available: https://zenodo.org/record/3888499. [Accessed: 26-Oct-2020]
[4] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018 [Online]. Available: https://data.humdata.org/dataset/south-africa-admin-level-1-boundaries